In this paper we have compared the cosmic ray intensity variations at ~1.5 GV rigidity with the corresponding time variations of the heliospheric current sheet tilt (HCST). These studies extend earlier work comparing neutron monitor variations with the HCST. In addition to the results of this earlier work we have found that (1) the delay of the cosmic ray intensity changes relative to the HCST changes is much less in 11-year cycles starting in a negative solar magnetic cycles. (2) During the specific periods of actual changeover of the solar magnetic field from positive to negative polarity, the cosmic ray intensity decrease is ~50% of the total 11-year cycle intensity decrease. During the changeover from negative to positive polarity, the entire cosmic ray 11-year decrease has almost fully occurred before the polarity changeover. (3) In 11-year modulation cycles starting in a negative polarity period, the regression coefficient between the cosmic ray intensity and tilt is ~0.9% per degree of tilt during both the decreasing and increasing phases. In the 11-year modulation cycles starting in a positive polarity cycle, the regression coefficient is much smaller, only ~0.4% per degree during much of the cycle; then it becomes much steeper toward the end of the cycle. These features are discussed in terms of current models for cosmic ray modulation that include diffusion, convection, drifts, and the wavy current sheet.